Existing growth methods produce single-walled carbon nanotubes (SWCNTs) with a range of structures and electronic properties, but many potential applications require pure nanotube samples. Density gradient ultracentrifugation (DGU) has recently emerged as a technique for sorting as-grown mixtures of single-walled nanotubes into their distinct ( n,m ) structural forms, but this approach has been limited to samples containing only a small number of nanotube structures, and has often required repeated DGU processing. For the first time, it has been shown that the use of tailored nonlinear density gradient ultracentrifugation (NDGU) can significantly improve DGU separations. This new sorting process readily separated highly polydisperse samples of SWCNTs grown by the HiPco method in a single step to give fractions enriched in any of ten different ( n,m ) species. In addition, minor variants of the method allowed separation of the minor-image isomers (enantiomers) of seven ( n,m ) species. Optimization of this new approach was aided by the development of instrumentation that spectroscopically mapped nanotube contents inside undisturbed centrifuge tubes. Besides, sorted nanotube samples enabled the discovery of novel oxygen-doped SWCNTs with remarkable photophysical properties. Modified nanotube samples were produced using mild oxidation of SWCNTs with ozone followed by a photochemical conversion step that induced well-defined changes in emissive properties. As demonstrated for a set of ten separated SWCNT ( n,m ) structures, chemically altered nanotubes possess slightly lower band gap energies with correspondingly longer photoluminescence wavelengths. Treated samples showed distinct, structure-specific near-infrared fluorescence at wavelengths 10 to 15% longer than the pristine semiconducting SWCNTs. Quantum chemical modeling suggests that dopant sites harvest light energy absorbed in undoped nanotube regions by trapping mobile excitons. The oxygen-doped SWCNTs are much easier to detect and image in biological specimen than pristine SWCNTs because they give stronger near-IR emission and do not absorb at the shifted emission wavelength. This novel modification of SWCNT properties may lead to new optical and electronic applications, as it provides a way to change optical band gaps in whole nanotubes or in selected sections.